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Mat. Vopr. Kriptogr., 2013, Volume 4, Issue 1, Pages 77–86 (Mi mvk74)  

This article is cited in 2 scientific papers (total in 2 papers)

On the numbers of equivalent tuples sets in a sequence of independent random variables

V. G. Mihailova, A. M. Shoitovb

a Steklov Mathematical Institute of RAS, Moscow
b Academy of Cryptography of the Russian Federation, Moscow

Abstract: Let $\mathbf X$ be a sequence of $n+s-1$ polynomial trials with $N$ outcomes. Limit joint distributions of the numbers of $r$-sets of equivalent $s$-tuples in $\mathbf X$ are proved. Two types of conditions on the parameters $n,N\to\infty$, $s<N$ are considered. Under the conditions of the first type the mean number of $s$-tuples with coinciding outcomes is bounded. Under the conditions of the second type the mean number of $s$-tuples without concidings is bounded.

Key words: polynomial trials, equivalent tuples, compound Poisson distribution.

DOI: https://doi.org/10.4213/mvk74

Full text: PDF file (120 kB)
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Document Type: Article
UDC: 519.212.2+519.214.5
Received 03.X.2012

Citation: V. G. Mihailov, A. M. Shoitov, “On the numbers of equivalent tuples sets in a sequence of independent random variables”, Mat. Vopr. Kriptogr., 4:1 (2013), 77–86

Citation in format AMSBIB
\Bibitem{MikSho13}
\by V.~G.~Mihailov, A.~M.~Shoitov
\paper On the numbers of equivalent tuples sets in a~sequence of independent random variables
\jour Mat. Vopr. Kriptogr.
\yr 2013
\vol 4
\issue 1
\pages 77--86
\mathnet{http://mi.mathnet.ru/mvk74}
\crossref{https://doi.org/10.4213/mvk74}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. D. Gusev, L. A. Miroshnichenko, N. V. Salomatina, “Strukturnye analogii v simvolnykh posledovatelnostyakh razlichnoi yazykovoi prirody”, Mashinnoe obuchenie i analiz dannykh, 1:10 (2014), 1407–1422  elib
    2. V. G. Mikhailov, “On the probability of existence of substrings with the same structure in a random sequence”, Discrete Math. Appl., 27:6 (2017), 377–386  mathnet  crossref  crossref  mathscinet  isi  elib
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